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Is there allready an implementation for Sine Transient Noise Separation of audio signals?

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Hi guys,
I'm looking for an existing implementation for a three-components decomposition of audio signals.
The idea of separate a signal into three components, one for the Sinusoidal part, one for the transients and one for the Residual (these models are often called STN models), is described in "A Review on Techniques for the Extraction of Transients in Musical Signals" by Laurent Daudet. Related methods, mentioned in this paper, include the "Time-Frequency Jigsaw Puzzle", the "Matching Pursuit" and the "Fast Iterated Reweighted Sparsifier".
Does anyone know of any functions or existing code related to this topic?
Thanks for your help.

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Accepted Answer

Stefanie Schwarz
Stefanie Schwarz on 13 Mar 2020
Edited: Stefanie Schwarz on 13 Mar 2020
It appears that a "Matching Pursuit" method is shipped with Wavelet Toolbox:
Refer to the following documentation page for more information regarding Denoising of Signals and Images:

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